Gentle introduction to social networks in R

Prof. Jose Manuel MAGALLANES.

• Professor at Pontificia Universidad Católica del Peru
• Senior Data Scientist at eScience Institute, University of Washington

---

CONTENTS:

1. Network Creation from dataframes

These data frames have been previously prepared, based on the data from 50 influential people in Seattle tech to follow on Twitter. The file can be seen here, and includes 3 sheets:

• Network as two columns representing edges.
• Network as adjacency matrix.
• Attributes of the Network nodes.

rm(list = ls())
##
fileLink='https://github.com/eScience-UW/gentleIntro_networks/raw/main/data/seattleTop.xlsx'

edges=rio::import(fileLink, which = 'edges') 
adjacency=rio::import(fileLink, which = 'adjacency')
attributes=rio::import(fileLink,which ="attributes")

Use the previous dataframes to create the network:

• From the edges:

library(igraph) # package needed

## 
## Attaching package: 'igraph'

## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum

## The following object is masked from 'package:base':
## 
##     union

EliteNet=graph_from_data_frame(edges, directed = F)

summary(EliteNet)

## IGRAPH 4205504 UN-- 46 393 -- 
## + attr: name (v/c)

• From adjacency matrix:

#prepare matrix
row.names(adjacency)=adjacency[,1] #first column for index
adjacency=adjacency[,-1] # deleting the first column
adjacencyMatrix=as.matrix(adjacency) 

# the making...
EliteNet=graph_from_adjacency_matrix(adjacencyMatrix,mode="undirected")


summary(EliteNet)

## IGRAPH f973939 UN-- 46 393 -- 
## + attr: name (v/c)

See inside:

V(EliteNet)

## + 46/46 vertices, named, from f973939:
##  [1] rachelerman     mattmcilwain    DaveParkerSEA   toddbishop     
##  [5] ashannstew      LeslieFeinzaig  akipman         matt_oppy      
##  [9] gilbert         juliesandler    BradSmi         crashdev       
## [13] ShaunaCausey    john_gabbert    moniguzman      mattmday       
## [17] Rich_Barton     daryn           lovelletters    etzioni        
## [21] MissDestructo   heatherredman   danshapiro      medinism       
## [25] KieranSnyder    hadip           RajSinghSeattle funcOfJoe      
## [29] kirbywinfield   stevesi         Ryanintheus     sonalpmane     
## [33] SoGulley        2morrowknight   jinman          tarah          
## [37] Jenerationy     lanctot         Kristen_Hammy   nhuntwalker    
## + ... omitted several vertices

E(EliteNet)

## + 393/393 edges from f973939 (vertex names):
##  [1] rachelerman--mattmcilwain    rachelerman--DaveParkerSEA  
##  [3] rachelerman--toddbishop      rachelerman--ashannstew     
##  [5] rachelerman--LeslieFeinzaig  rachelerman--akipman        
##  [7] rachelerman--matt_oppy       rachelerman--gilbert        
##  [9] rachelerman--juliesandler    rachelerman--BradSmi        
## [11] rachelerman--crashdev        rachelerman--ShaunaCausey   
## [13] rachelerman--john_gabbert    rachelerman--moniguzman     
## [15] rachelerman--mattmday        rachelerman--Rich_Barton    
## [17] rachelerman--daryn           rachelerman--lovelletters   
## [19] rachelerman--etzioni         rachelerman--MissDestructo  
## + ... omitted several edges

2. Adding Attributes

Attributes are added using vectors:

# edges
E(EliteNet)$weight=1
# EliteNet=set_edge_attr(EliteNet,"weight", value = 1)

#nodes
V(EliteNet)$male=attributes$male
V(EliteNet)$followers=attributes$followers
# EliteNet=set_vertex_attr(EliteNet, "followers", value=attributes$followers)

##
# E(EliteNet)$weight
# edge_attr_names(EliteNet)
# V(EliteNet)$followers
# vertex_attr_names(EliteNet)
summary(EliteNet)

## IGRAPH f973939 UNW- 46 393 -- 
## + attr: name (v/c), male (v/n), followers (v/n), weight (e/n)

You can use attributes to color nodes:

library(ggraph)

## Loading required package: ggplot2

base=ggraph(graph = EliteNet)

## Using "stress" as default layout

base + geom_node_label(aes(label = name,
                           color=as.factor(male)),
                       repel = TRUE,show.legend = F) + 
       geom_edge_link(alpha=0.1) + 
       scale_color_manual(values = c('red','blue'))

## Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

3. Exploring the Network

• Connectedness: A network is “connected” if there exists a path between any pair of nodes (undirected networks).

is_connected(EliteNet)

## [1] TRUE

• Density: from 0 to 1, where 1 makes it a ‘complete’ network: there is a link between every pair of nodes.

graph.density(EliteNet)

## [1] 0.3797101

• Diameter: When two vertices are connected, one can reach the other using multiple egdes. The geodesic is the shorthest path between two connected vertices. Then, the diameter, is the maximum geodesic in a network.

diameter(EliteNet)

## [1] 3

• Assortativity: it is a measure to see if nodes are connecting to other nodes similar to themselves. Closer to 1 means higher assortativity, closer to -1 diassortativity; while 0 is no assortativity.

  • Degree assortativity: tendency for highly connected nodes to be connected among themselves.

assortativity_degree(EliteNet,directed=F)

## [1] -0.2541114

- Categorical assortativity: tendency for nodes with other nodes sharing the same category.

assortativity_nominal(EliteNet,as.factor(V(EliteNet)$male),directed = F)

## [1] 0.04310211

- Assortativity (numerical): 

assortativity(EliteNet,V(EliteNet)$followers,directed = T)

## [1] -0.04515662

4. Exploration of Network nodes

• The eigenvector of a vertex will tell you how well connected is a vertex; that is, vertices with the highest values are considered the most influential as they are connected to vertices that are also well connected.

• The closeness of a vertex will tell you how close is a vertex to every other vertex. A vertex with high closeness can share information faster than the rest.

• The betweeness of a vertex will tell you how critical is a vertex to connect vertex that are not connected directly.

eigen=eigen_centrality (EliteNet,scale=F)$vector

close=closeness(EliteNet,normalized=T)

betw=betweenness(EliteNet,normalized=T)

DFCentrality=as.data.frame(cbind(eigen,close,betw),stringsAsFactors = F)
names(DFCentrality)=c('Eigenvector','Closeness','Betweenness')

DFCentrality$person=row.names(DFCentrality)
row.names(DFCentrality)=NULL

library(ggplot2)
ggplot(DFCentrality, aes(x=Betweenness, y=Closeness)) + 
    theme_classic() +
    geom_text(aes(label=person,size=Eigenvector),show.legend = F,alpha=0.5) 

The previous results tells us that two people are salient:

HubNodes=dplyr::top_n(DFCentrality,2,Eigenvector)$person
HubNodes

## [1] "DaveParkerSEA" "toddbishop"

Let’s highlight those guys:

NodeCount=length(V(EliteNet))

V(EliteNet)$label=''

for (index in seq(1:NodeCount)){
    currentName=V(EliteNet)$name[index]
    if (currentName%in%HubNodes){
            V(EliteNet)$label[index]=currentName
    }
}

library(ggraph)

base=ggraph(graph = EliteNet)

## Using "stress" as default layout

base  + geom_node_label(aes(label = label), 
                        repel = TRUE,
                        show.legend = F,
                        color='red') + 
         geom_edge_link(alpha=0.1)

5. Communities

RandomNet <- erdos.renyi.game(length(V(EliteNet)), 0.5)

• Transitivity: How probable is that two nodes with a common connection, are also connected.

transitivity(RandomNet)

## [1] 0.5250664

transitivity(EliteNet)

## [1] 0.5504253

• Partition

Set of nodes that belong to a group. The hard problems is to decide what node goes where:

# edges that will partition the net
mincut=igraph::min_cut(EliteNet, value.only = FALSE)$cut
mincut

## + 2/393 edges from f973939 (vertex names):
## [1] DaveParkerSEA--2morrowknight MissDestructo--2morrowknight

# ends() gives you a matrix, unique() keeps non duplicates
labelsEdgesBye=unique(as.vector(ends(EliteNet,mincut))) # flattening
labelsEdgesBye

## [1] "DaveParkerSEA" "MissDestructo" "2morrowknight"

EliteNet_cut=delete_edges(EliteNet,mincut)

SubSetLabels=ifelse(V(EliteNet)$name%in%labelsEdgesBye,V(EliteNet)$name,"")

base=ggraph(graph =EliteNet_cut ) + geom_edge_link(alpha=0.2)

## Using "stress" as default layout

base + geom_node_label(aes(label=SubSetLabels),repel = T) 

The girvan_newman algorithm is based on creating partitions using the centrality of nodes to create partition too. We can create something similar to the last result like this:

# creating all partitions
partition_girvanNewman_all <- edge.betweenness.community(EliteNet,merges = T)

## Warning in edge.betweenness.community(EliteNet, merges = T): At
## core/community/edge_betweenness.c:493 : Membership vector will be selected
## based on the highest modularity score.

# the first partition
partition_girvanNewman_first= cut_at(partition_girvanNewman_all,2)

ColorIndex=partition_girvanNewman_first

base=ggraph(graph =EliteNet) + geom_edge_link(alpha=0.2)

## Using "stress" as default layout

base + geom_node_point(aes(color=ColorIndex), show.legend = F, size=4) +
    geom_node_text(aes(label=label,color=ColorIndex),repel = T,show.legend = F) 

A more complex algorithm is the Louvain:

partition_louvain=cluster_louvain(EliteNet)

V(EliteNet)$louvain=membership(partition_louvain)

base=ggraph(graph =EliteNet) + geom_edge_link(alpha=0.2)

## Using "stress" as default layout

base + geom_node_point(aes(color=as.factor(louvain)), show.legend = F, size=4) 

a_partition_girvanNewman=cut_at(partition_girvanNewman_all,max(membership(partition_louvain)))

• Modularity:

If we get positive values (being 1 the top value), we could consider there are good community structures (wiki). The higher modularity the connections between the nodes are dense within a partition but sparse between nodes in different partitions.

modularity(EliteNet, a_partition_girvanNewman)

## [1] -0.0002751717

modularity(EliteNet,membership(partition_louvain))

## [1] 0.1106546

V(EliteNet)$louvain=membership(partition_louvain)
V(EliteNet)$girvanNewman=membership(partition_louvain)

write_graph(EliteNet, "EliteNet_R.graphml", "graphml")